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Decaying oscillations Let a > 0 and b be real numbers. Use
Chapter 7, Problem 69E(choose chapter or problem)
QUESTION:
Decaying oscillations Let a > 0 and b be real numbers. Use integration to confirm the following identities.
a. \(\int_{0}^{\infty} e^{-a x} \cos b x \ d x=\frac{a}{a^{2}+b^{2}}\)
b. \(\int_{0}^{\infty} e^{-a x} \sin b x \ d x=\frac{b}{a^{2}+b^{2}}\)
Questions & Answers
QUESTION:
Decaying oscillations Let a > 0 and b be real numbers. Use integration to confirm the following identities.
a. \(\int_{0}^{\infty} e^{-a x} \cos b x \ d x=\frac{a}{a^{2}+b^{2}}\)
b. \(\int_{0}^{\infty} e^{-a x} \sin b x \ d x=\frac{b}{a^{2}+b^{2}}\)
ANSWER:Solution:-
Step1
Given that
Let a > 0 and b be real numbers.
Step2
To find
Use integration to confirm the following identities.
a.
b.
Step3
a.